Turbulence in a skewed three‐dimensional wall‐bounded shear flow: effect of mean vorticity on structure modification

Mean‐flow three‐dimensionalities affect both the turbulence level and the coherent flow structures in wall‐bounded shear flows. A tailor‐made flow configuration was designed to enable a thorough investigation of moderately and severely skewed channel flows. A unidirectional shear‐driven plane Couette flow was skewed by means of an imposed spanwise pressure gradient. Three different cases with 8°, 34°and 52°skewing were simulated numerically and the results compared with data from a purely two‐dimensional plane Couette flow. The resulting three‐dimensional flow field became statistically stationary and homogeneous in the streamwise and spanwise directions while the mean velocity vector V and the mean vorticity vector Ω remained parallel with the walls. Mean flow profiles were presented together with all components of the Reynolds stress tensor. The mean shear rate in the core region gradually increased with increasing skewing whereas the velocity fluctuations were enhanced in the spanwise direction and reduced in the streamwise direction. The Reynolds shear stress is known to be closely related to the coherent flow structures in the near‐wall region. The instantaneous and ensemble‐averaged flow structures were turned by the skewed mean flow. We demonstrated for the medium‐skewed case that the coherent structures should be examined in a coordinate system aligned with V to enable a sound interpretation of 3D effects. The conventional symmetry between Case 1 and Case 2 vortices was broken and Case 1 vortices turned out to be stronger than Case 2. This observation is in conflict with the common understanding on the basis of the spanwise (secondary) mean shear rate. A refined model was proposed to interpret the structure modifications in three‐dimensional wall‐flows. What matters is the orientation of the mean vorticity vector Ω relative to the vortex vorticity vector ω _v, that is, the sign of Ω · ω _v. In the present situation, Ω · ω _v > 0 for the Case 1 vortices causing a strengthening relative to the Case 2 vortices. Copyright © 2011 John Wiley & Sons, Ltd.     

Structure of near wall turbulence downstream of a wall mounted protrusion: an interesting Reynolds stress suppression phenomena

A local suppression in the generation of near wall Reynolds stress is achieved by modifying the buffer region and sublayer (y ⁺ <30) of a turbulent pipe flow with a 16.4 wall unit high wall mounted protrusion. Multi-component, multi-point, time resolved laser Doppler velocimetry measurements are made in the undisturbed and modified ARL/PSU glycerin tunnel pipe flow at a Reynolds number of approximately 10000. A downstream converging flow field is produced by the divergence of the approaching mean flow around the protrusion. A pair of counter-rotating vortices, 15 wall units in diameter with common flow down, are generated by the protrusion and also contribute to the wall directed flow convergence. The convergence region is 15 wall units high and more than 100 wall units long and appears to decouple the near wall region from the outer turbulent wall layer. Locally, turbulent velocity fluctuations in the form of Reynolds stress producing events, sweeps and ejections, are retarded within this region. This results in a reduction in near wall uv Reynolds stress and local wall shear. Interestingly, the counter-rotating vortices act to increase turbulent diffusion in a manner which is uncorrelated with Reynolds stress generation.     

Large eddy simulation of flows after a bluff body: Coherent structures and mixing properties

This paper performs large eddy simulations (LES) to investigate coherent structures in the flows after the Sydney bluff-body burner, a circular bluff body with an orifice at its center. The simulations are validated by comparison to existing experimental data. The Q function method is used to visualize the instantaneous vortex structures. Three kinds of structures are found, a cylindrical shell structure in the outer shear layer, a ring structure and some hairpin-like structures in the inner shear layer. An eduction scheme is employed to investigate the coherent structures in this flow. Some large streaks constituted by counter-rotating vortices are found in the outer shear layer and some well-organized strong structures are found in the inner shear layer. Finally, the influences of coherent structures on scalar mixing are studied and it is shown that scalar in the recirculation region is transported outward by coherent structures.     

Wake of a cylinder: a paradigm for energy harvesting with piezoelectric materials

Short-length piezoelectric beams were placed in the wake of a circular cylinder at high Reynolds numbers to evaluate their performance as energy generators. The coherent vortical structures present in this flow generate a periodic forcing on the beam which when tuned to its resonant frequency produces maximum output voltage. There are two mechanisms that contribute to the driving forcing of the beam. The first mechanism is the impingement of induced flow by the passing vortices on one side of the beam, and the second is the low pressure core region of the vortices which is present at the opposite side of the beam. The sequence of these two mechanisms combined with the resonating conditions of the beam generated maximum energy output which was also found to vary with the location in the wake. The maximum power output was measured when the tip of the beam is about two diameters downstream of the cylinder. This power drops off the center line of the wake and decays with downstream distance as (x/D)^−3/2.     

Modelling the time dependent flow over riblets in the viscous wall region

The flow over riblets is examined computationally using a time dependent model of the viscous wall region. This 2 1/2 D model, developed by Hatziavramidis and Hanratty (1979) and modified by Nikolaides (1984) and Chapman and Kuhn (1981, 1986) assumes homogeneity in the streamwise direction so that the flow is solved only in the cross-sectional plane. The flow at the upper boundary of the computational domain (y ⁺ 40) is described using a streamwise eddy model consisting of two scales, one of the streak spacing (⁺ 100), which dominates vertical momentum transport, and a larger scale that accounts for the influence of large outer flow eddies.The protrusion height concept (Bechert and Bartenwerfer, 1989) is used to define ay ⁺=0 location for surfaces with riblets. A control volume finite element method utilizing triangular meshes is used to exactly fit the riblet cross-sectional geometry. Results obtained using fairly large riblets compare well with the limited experimental evidence available. Observations of the transient flow suggest that the riblets interact with the near-wall streamwise vortices, weakening them by the generation of intermittent secondary vortices within the riblet valleys. The riblets also appear to limit the lateral spread of inrushes towards the wall and retain low momentum fluid in the riblet valleys effectively isolating much of the wall from such inrushes.     

Flow field analysis of a turbulent boundary layer over a riblet surface

The near-wall flow structures of a turbulent boundary layer over a riblet surface with semi-circular grooves were investigated experimentally for the cases of drag decreasing (s ⁺=25.2) and drag increasing (s ⁺=40.6). One thousand instantaneous velocity fields over riblets were measured using the velocity field measurement technique and compared with those above a smooth flat plate. The field of view was 6.75 × 6.75 mm² in physical dimension, containing two grooves. Those instantaneous velocity fields were ensemble averaged to get turbulent statistics including turbulent intensities and turbulent kinetic energy. To see the global flow structure qualitatively, flow visualization was also carried out using the synchronized smoke-wire technique under the same experimental conditions. For the case of drag decreasing (s ⁺=25.2), most of the streamwise vortices stay above the riblets, interacting with the riblet tips frequently. The riblet tips impede the spanwise movement of the streamwise vortices and induce secondary vortices. The normalized rms velocity fluctuations and turbulent kinetic energy are small near the riblet surface, compared with those over a smooth flat plate. Inside the riblet valleys, these are sufficiently small that the increased wetted surface area of the riblets can be compensated. In addition, in the outer region (y ⁺ > 30), these values are almost equal to or slightly smaller than those for the smooth plate. For the case of drag increasing (s ⁺=40.6), however, most of the streamwise vortices stay inside the riblet valleys and contact directly with the riblet surface. The high-speed down-wash flow penetrating into the riblet valley interacts actively with the wetted riblet surface and increases the skin friction. The rms velocity fluctuations and turbulent kinetic energy have larger values compared with those over a smooth flat plate. Received: 24 March 1999/Accepted: 10 March 2000     

Time resolved investigations on flow field and quasi wall shear stress of an impingement configuration with pulsating jets by means of high speed PIV and a surface hot wire array

The effects of jet pulsation on flow field and quasi wall shear stress of an impingement configuration were investigated experimentally. The excitation Strouhal number and amplitude were varied as the most influential parameters. A line-array with three submerged air jets, and a confining plate were used. The flow field analysis by means of time resolved particle image velocimetry shows that the controlled excitation can considerably affect the near-field flow of an impinging jet array. These effects are visualized as organization of the coherent flow structures. Augmentation of the Kelvin–Helmholtz vortices in the jet shear layer depends on the Strouhal number and pulsation magnitude and can be associated with pairing of small scale vortices in the jet. A total maximum of vortex strength was observed when exciting with Sr = 0.82 and coincident high amplitudes.Time resolved interaction between impinging vortices and impingement plate boundary layer due to jet excitation was verified by using an array of 5 μm surface hot wires. Corresponding to the global flow field modification due to periodic jet pulsation, the impact of the vortex rings on the wall boundary layer is highly influenced by the above mentioned excitation parameters and reaches a maximum at Sr = 0.82.     

LES of turbulent flow in a concentric annulus with rotating outer wall

Fully-developed turbulent flow in a concentric annulus, r₁/r₂ = 0.5, Re_h = 12,500, with the outer wall rotating at a range of rotation rates N = U_θ,wall/U_b from 0.5 up to 4 is studied by large-eddy simulations. The focus is on the effects of moderate to very high rotation rates on the mean flow, turbulence statistics and eddy structure. For N up to ∼2, an increase in the rotation rate dampens progressively the turbulence near the rotating outer wall, while affecting only mildly the inner-wall region. At higher rotation rates this trend is reversed: for N = 2.8 close to the inner wall turbulence is dramatically reduced while the outer wall region remains turbulent with discernible helical vortices as the dominant turbulent structure. The turbulence parameters and eddy structures differ significantly for N = 2 and 2.8. This switch is attributed to the centrifuged turbulence (generated near the inner wall) prevailing over the axial inertial force as well as over the counteracting laminarizing effects of the rotating outer wall. At still higher rotation, N = 4, the flow gets laminarized but with distinct spiralling vortices akin to the Taylor–Couette rolls found between the two counter-rotating cylinders without axial flow, which is the limiting case when N approaches to infinity. The ratio of the centrifugal to axial inertial forces, Ta/Re² ∝ N² (where Ta is the Taylor number) is considered as a possible criterion for defining the conditions for the above regime change.     

Experimental Investigation of Separated Shear Flow under Subharmonic Perturbations over a Backward-Facing Step

Subharmonic-perturbed shear flow downstream of a two-dimensional backward-facing step was experimentally investigated. The Reynolds number was Re_h = 2.0 ×10⁴, based on free-stream velocity and step height. Planar 2D-2C particle image velocimetry was employed to measure the separating and reattaching flow in the horizontal-vertical plane in the center position. The subharmonic perturbations were generated by an oscillating flap which was implemented over the step edge and driven by periodic Ampere force. The subharmonic frequency was 55 Hz as the half of the fundamental frequency of the turbulent shear layer. As a result of the subharmonic perturbations, the size of recirculation region behind the backward-facing step is reduced and the time-averaged reattachment length is 31.0% shorter than that of the natural flow. The evolution of vortices, including vortex roll-up, growth and breakdown process, is analyzed by using phase-averaging, cross-correlation function and proper orthogonal decomposition. It is found that Reynolds shear stress is considerably increased in which the vortices roll up and then break down further downstream. In particular, rapid growth of vortices based on the “step mode” occurs at approximate half of the recirculation region, caused by in interaction between the shear layer and the recirculation region. Furthermore, the coherent structures, which are represented by a phase-correlated POD mode pair, are reconstructed in phases in order to show regular patterns of the subharmonic-perturbed coherent structures.     

Generation of coherent structures in supersonic flow past a finite-span flat plate

The formation of coherent structures on a flat plate in a supersonic flow is numerically investigated both in the case of strong shock incidence on the plate and in the problem of oncoming harmonic waves having an intensity of 1–5% of the freestream pressure P ₀. The same mechanism of the coherent structure formation is noticed in both nonstationary problems; it is due to the manifestation of the secondary instability generated in the gas flow owing to the influence of the vortices formed at the lateral edges of the plate. An analysis of the incident wave enhancement at the rear of the plate is made for different wave intensities and wavelength to plate width ratios. The flow patterns in the plate wake indicate the generation of an intense expansion wave in this region, which accelerates the gas flow to the freestream velocity.     

Modelling the time-dependent flow over riblets in the viscous wall region

The flow over drag reducing riblets is examined computationally using a time-dependent model of the viscous wall region. The flow at the upper bound of the computational domain (y ⁺?40) is described using a streamwise eddy model consisting of two scales. A control-volume finite-element method utilizing triangular meshes is used to exactly fit the riblet cross-sectional geometry. Observations of the transient flow conditions suggest that the riblets limit the lateral spread of fluid inrushes towards the wall and retain low momentum fluid in the riblet valleys effectively isolating much of the wall from such inrushes. The generation of intermittent secondary vortices within the riblet valleys also occurs; however, these appear to be quite weak and fairly short-lived.     

Influence of wavy surfaces on coherent structures in a turbulent flow

We describe how outer flow turbulence phenomena depend on the interaction with the wall. We investigate coherent structures in turbulent flows over different wavy surfaces and specify the influence of the different surface geometries on the coherent structures. The most important contribution to the turbulent momentum transport is attributed to these structures, therefore this flow configuration is of large engineering interest. In order to achieve a homogeneous and inhomogeneous reference flow situation two different types of surface geometries are considered: (1) three sinusoidal bottom wall profiles with different amplitude-to-wavelength ratios of α = 2a/Λ = 0.2 (Λ = 30 mm), α = 0.2 (Λ = 15 mm), and α = 0.1 (Λ = 30 mm); and (2) a profile consisting of two superimposed sinusoidal waves with α = 0.1 (Λ = 30 mm). Measurements are carried out in a wide water channel facility (aspect ratio 12:1). Digital particle image velocimetry (PIV) is performed to examine the spatial variation of the streamwise, spanwise and wall-normal velocity components in three measurement planes. Measurements are performed at a Reynolds number of 11,200, defined with the half channel height h and the bulk velocity U _B. We apply the method of snapshots and perform a proper orthogonal decomposition (POD) of the streamwise, spanwise, and wall-normal velocity components to extract the most dominant flow structures. The structure of the most dominant eigenmode is related to counter-rotating, streamwise-oriented vortices. A qualitative comparison of the eigenfunctions for different sinusoidal wall profiles shows similar structures and comparable characteristic spanwise scales Λ _z = 1.5 H in the spanwise direction for each mode. The scale is observed to be slightly smaller for α = 0.2 (Λ = 15 mm) and slightly larger for α = 0.2 (Λ = 30 mm). This scaling for the flow over the basic wave geometries indicates that the size of the largest structures is neither directly linked to the solid wave amplitude, nor to the wavelength. The characteristic spanwise scale of the dominant eigenmode for the developed flow over the surface consisting of two superimposed waves reduces to 0.85 H. However, a scale in the order of 1.3 H is identified for the second mode. The eigenvalue spectra for the superimposed waves is much broader, more modes contribute to the energy-containing range. The turbulent flow with increased complexity of the bottom surface is characterized by an increased number of dominant large-scale structures with different spanwise scales.     

Stereoscopic and tomographic PIV of a pitching plate

This paper applies particle image velocimetry (PIV) to a simplified, canonical, pitch-hold-return problem of a pitching plate in order to gain some understanding of how three dimensionality develops in such flows. Data from a progression of PIV studies, from stereoscopic PIV yielding three-component, two-dimensional (3C-2D) data to tomographic PIV yielding three-component, three-dimensional (3C-3D) data are presented thus providing progressively more detailed information. A comparison of results is made between the two techniques. The PIV study is performed in a water tunnel facility with cross-sectional area 500 × 500 mm, and involves a full-span (nominally two-dimensional) plate, suspended between a wall end boundary condition and a free surface, pitching at a dimensionless pitch rate of K _c  = 0.93 in flow at Re = 7,500. Results demonstrate the existence of spanwise flows in both the leading edge and trailing edge vortices, but with strong directionality in the leading edge vortex towards the wall end boundary condition. Observations of instantaneous flow patterns suggest also the existence of three-dimensional coherent vortex filament structures in the outer regions of the leading edge vortex.     

Evolution of vortex structures in an electromagnetically excited separated flow

Time periodic wall parallel Lorentz forces have been used to excite the separated flow on the suction side of an inclined flat plate. Experiments for a Reynolds number of 10⁴ and an angle of attack of α = 13° are reported. The controlled flow is characterised by a small number of relatively large scale vortices, which are related to the control mechanism. The influence of the main parameters, i.e. the excitation frequency, amplitude and wave form on the suction side flow structures was investigated by analysing time resolved particle image velocimetry (TR-PIV) measurements using continuous wavelet analysis for vortex detection and characterisation. Statistical analysis of the coherent structures of the flow was performed on a large amount of data samples.     

Reynolds Number Effects on the Coherent Dynamics of the Turbulent Horseshoe Vortex System

The adverse pressure gradient induced by a surface-mounted obstacle in a turbulent boundary layer causes the approaching flow to separate and form a dynamically rich horseshoe vortex system (HSV) in the junction of the obstacle with the wall. The Reynolds number of the flow (Re) is one of the important parameters that control the rich coherent dynamics of the vortex, which are known to give rise to low-frequency, bimodal fluctuations of the velocity field (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). We carry out detached eddy simulations (DES) of the flow past a circular cylinder mounted on a rectangular channel for Re = 2.0 × 10⁴ and 3.9 × 10⁴ (Dargahi, Exp Fluids 8:1–12, 1989) in order to systematically investigate the effect of the Reynolds number on the HSV dynamics. The computed results are compared with each other and with previous experimental and computational results for a related junction flow at a much higher Reynolds number (Re = 1.15 × 10⁵) (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). The computed results reveal significant variations with Re in terms of the mean-flow quantities, turbulence statistics, and the coherent dynamics of the turbulent HSV. For Re = 2.0 × 10⁴ the HSV system consists of a large number of necklace-type vortices that are shed periodically at higher frequencies than those observed in the Re = 3.9 × 10⁴ case. For this latter case the number of large-scale vortical structures that comprise the instantaneous HSV system is reduced significantly and the flow dynamics becomes quasi-periodic. For both cases, we show that the instantaneous flowfields are dominated by eruptions of wall-generated vorticity associated with the growth of hairpin vortices that wrap around and disorganize the primary HSV system. The intensity and frequency of these eruptions, however, appears to diminish rapidly with decreasing Re. In the high Re case the HSV system consists of a single, highly energetic, large-scale necklace vortex that is aperiodically disorganized by the growth of the hairpin mode. Regardless of the Re, we find pockets in the junction region within which the histograms of velocity fluctuations are bimodal as has also been observed in several previous experimental studies.     

On swirl development in a square cross-sectioned, S-shaped duct

The flow in a uniform square cross-sectioned, S-shaped duct was investigated experimentally, at Reynolds number (Re) = 4.73 × 10⁴ and 1.47 × 10⁵, using three S-ducts of different curvature and turning angle. The hydraulic diameter (D) for each S-duct is 150 mm. Besides studying the square cross-sectioned S-duct flow at moderately higher Re than current literature, the S-ducts’ geometry used in this study also have larger curvatures and higher turning angles than those reported in the literature. With surface pressure measurement and smoke wire flow visualization, flow separation at the inside wall of the first bend was detected. Using surface oil flow visualization on the bottom wall of the S-duct and cross-wires measurement at the duct exit, it is shown here that the swirl developed in the first bend was partly attenuated in the second bend due to the formation of swirl of opposite direction. The swirl of an opposite sign results in the formation of a clear dividing or separation line on the bottom wall (and top wall) of the duct. Additional flow features include the formation of streamwise vortices on the outer-wall of the second bend. These streamwise vortices can either be a pair of counter-rotating vortices or a single vortex. The formation mechanism of these streamwise vortices is explained using the Squire and Winter [J Aeronaut Sci 18(4):271–277, 1951] formula and it is shown that the said mechanism is applicable to both Re in the present study.     

Computational analysis and flow structure of a transitional separated-reattached flow over a surface mounted obstacle and a forward-facing step

Large-eddy simulation (LES) of transitional separating-reattaching flow on a two-dimensional square surface mounted obstacle and a forward facing step has been performed using a dynamic sub-grid scale model. The Reynolds number based on the uniform inlet velocity and the obstacle/step height is 4.5 × 10³. The mean LES results for both the obstacle and step flow compare reasonably well with the available experimental and DNS data.

The flow structures upstream of the surface-mounted obstacle (referred to hereafter as obstacle) and the forward-facing step (referred to hereafter as FFS) consist of unstable two-dimensional structures and coherent rib-shaped structures. These structures with the aid of 3D streamline visualisation strongly indicate that the upstream separation bubble is a closed one rather than an open one in the sense that there is little evidence to suggest that there is fluid injection from the upstream separation region into the downstream separated region for the two geometries. The spectra and time history for the velocities and pressure fields at locations immediately upstream of the obstacle and FFS (including the recirculation region) were analysed using both the Fourier and wavelet transforms and revealed the unsteady nature of the recirculation region upstream of the obstacle and FFS.

The transition process has been elucidated using both 2D and 3D flow visualisation of the flow. In both geometries (obstacle and FFS), the separated boundary layer downstream of the leading edge shows 2D nature and roll-up shortly downstream of the separation line leading to 2D K-H rolls to be shed from the leading edge. Coherent structures such as the λ-shaped and rib-like vortices commonly associated with a flat plate boundary layer and also found in the separated-reattached flow of a blunt leading edge plate aligned horizontally to a flow are not common in the separated-reattached flow over the obstacle and FFS.     

Synchronized analysis of an unsteady laminar flow downstream of a circular cylinder centred between two parallel walls using PIV and mass transfer probes

Experiments are carried out in the wake of a cylinder of d _c  = 10 mm diameter placed symmetrically between two parallel walls with a blockage ratio r = 1/3 and a Reynolds number varying between 75 ≤ Re ≤ 277. Particle image velocimetry is exerted to obtain the instantaneous velocity components in the cylinder wake. A snapshot proper orthogonal decomposition (POD) is also applied to these PIV results in order to extract the dominant modes through the implementation of an inhomogeneous filtering of these different snapshots, apart from an interpolation to estimate the wall shear rate at the lower wall downstream the cylinder. Mass transfer circular probes are placed at the lower wall downstream this obstacle so as to further determine the time evolution of the wall shear rate, by bringing the inverse method to bear on the convective-diffusion equation. Comparisons between the two synchronized techniques demonstrate that electrochemical method can give more accurate information about the coherent structures present in the flow and about the interaction of the von Kármán vortices with the walls of the tunnel as well. The comparison between the two measurement techniques in the flow regions concerns the spatiotemporal evolutions of the wall shear rate obtained from PIV measurements and the wall shear rate using mass transfer probes. Discrepancy between the PIV measurements and the electrochemical ones near the wall, where the secondary vortices P ₁′ are generated at wall, are caused by a PIV bias and a limitations of the singular mass transfer probes.     

后向台阶湍流拟序结构的实验研究

在水槽中用氢气泡法观测了一个后向台阶的回流区、再附区和边界层再生区的大涡和湍流团的发展,以及近壁区的流动结构,观察到大涡结构对湍流团产生的作用。